I don't know if this would fly with my council now (my son is only a Cub Scout) but when I got my Eagle *cough* 20 *cough* years ago, this would not have passed muster with our SM.
You currently have approval for your revised plan as you've mentioned it here? You say it was rejected once until you made changes, has it been fully approved with those changes?
The main things as you know are to plan, develop, and provide leadership. So as long as you have a leadership opportunity here, which I guess would be directing other scouts during the actual distribution event, then you technically have the requirements covered, but what could you do to expand it and make it more impactful?
How did you arrive at this? Did you come up with it before approaching them, or did you approach the community and ask what they needed help with, or a little of back and forth? Is there something beyond just passing out contact forms? Like having your scouts help them fill out information? Maybe making copies for them, or digitizing and e-mailing them, or laminating them? What is the problem you are trying to address? Is there a need for these people to have emergency contacts and they current don't? Could you expand this to bring in someone from the Red Cross to give a talk on emergency preparedness? What about raising money to put together emergency kits/first aid you could hand out?
I don't want to poo poo your project, and if you already have approval, then all the better, but I'm sure you could come up with more to do to make it more impactful/lasting and give more opportunities to direct/lead beyond the one shot flyer handout.